Are we observing an NSC in course of formation in the NGC 4654 galaxy?

We use direct N-body simulations to explore some possible scenarios for the future evolution of two massive clusters observed towards the centre of NGC 4654, a spiral galaxy with mass similar to that of the Milky Way. Using archival HST data, we obtain the photometric masses of the two clusters, M = 3 × 105 M= and M = 1.7 × 106 M=, their half-light radii, Reff ∼4 pc and Reff ∼6 pc, and their projected distances from the photometric centre of the galaxy (both <22 pc). The knowledge of the structure and separation of these two clusters (∼24 pc) provides a unique view for studying the dynamics of a galactic central zone hosting massive clusters. Varying some of the unknown cluster orbital parameters, we carry out several N-body simulations showing that the future evolution of these clusters will inevitably result in their merger. We find that, mainly depending on the shape of their relative orbit, they will merge into the galactic centre in less than 82 Myr. In addition to the tidal interaction, a proper consideration of the dynamical friction braking would shorten the merging times up to few Myr. We also investigate the possibility to form a massive nuclear star cluster (NSC) in the centre of the galaxy by this process. Our analysis suggests that for low-eccentricity orbits, and relatively long merger times, the final merged cluster is spherical in shape, with an effective radius of few parsecs and a mass within the effective radius of the order of 105,M⊙. Because the central density of such a cluster is higher than that of the host galaxy, it is likely that this merger remnant could be the likely embryo of a future NSC.